Question

If 3 tan $\theta$=4, find the value of $\frac{4cos\theta -sin\theta }{2cos\theta +sin\theta }$

Answer 1

3tan$\theta$ = 4
tan$\theta$ = 4/3= p/b
p= 4 , b= 3 , h= ?
we know that,
h²= (p)²+ (b)²
h²= (4)²+(3)²
h²= 16+9= 25
h= ✓25=5
Therefore,
sin$\theta$ = p/h = 4/5
cos$\theta$ = b/h = 3/5
Therefore,
=$\frac{4cos\theta -sin\theta }{2sin\theta +6cos\theta }$
=$\frac{4\times \left(3/5\right)-\left(4/5\right)}{2\left(4/5\right)+6\left(3/5\right)}$= 4/13